A person pushes a 15.0 kg lawn mower at constant speed with a force of 77.0 N directed along the handle, which is at an angle of θ = 49.0° to the horizontal .
(a) Draw the free-body diagram showing all forces acting on the mower. (Do this on paper. Your instructor may ask you to turn in this diagram.)
(b) Calculate the horizontal retarding force on the mower
(c) Calculate the normal force exerted vertically upward on the mower by the ground.
(d) Calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.0 m/s in 2.0 seconds (assuming the same retarding force).
Plzzzzzz help me...
(a) The free-body diagram of the lawn mower will include the following forces:
1. The force exerted by the person pushing the mower along the handle (77.0 N), directed at an angle of 49.0° to the horizontal.
2. The weight of the lawn mower (mg), directed vertically downward.
3. The normal force exerted by the ground, directed vertically upward.
4. The horizontal retarding force opposing the motion of the lawn mower.
(b) To calculate the horizontal retarding force on the mower, we need to use the information given. Since the mower is moving at a constant speed, the retarding force must be equal in magnitude and opposite in direction to the pushing force along the handle.
Therefore, the horizontal retarding force is 77.0 N.
(c) To calculate the normal force exerted vertically upward on the mower, we need to consider the equilibrium of forces in the vertical direction. At constant speed, the vertical forces must balance each other.
The weight of the lawn mower is given by:
Weight = mass × acceleration due to gravity = 15.0 kg × 9.8 m/s^2 = 147 N.
Since the vertical forces are balanced, the normal force exerted by the ground is equal in magnitude but opposite in direction to the weight of the lawn mower:
Normal force = 147 N.
(d) To calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.0 m/s in 2.0 seconds, we need to use Newton's second law of motion:
Force = mass × acceleration.
The mass of the lawn mower is given as 15.0 kg, and the acceleration can be calculated using the formula:
Acceleration = (final velocity - initial velocity) / time.
Acceleration = (1.0 m/s - 0 m/s) / 2.0 s = 0.5 m/s^2.
Now, we can calculate the force required:
Force = mass × acceleration = 15.0 kg × 0.5 m/s^2 = 7.5 N.
Therefore, the person must exert a force of 7.5 N on the lawn mower to accelerate it from rest to 1.0 m/s in 2.0 seconds.
Sure, I'm happy to help you with this problem! Let's go through each part step by step.
(a) To draw the free-body diagram, we need to identify all the forces acting on the lawn mower.
- The force of gravity acts straight downward and has a magnitude of mg, where m is the mass of the mower (15.0 kg) and g is the acceleration due to gravity (9.8 m/s^2).
- The normal force exerted by the ground opposes the force of gravity and acts perpendicular to the ground. We'll call this force N.
- The force applied by the person is directed along the handle at an angle of 49.0° to the horizontal. We'll call this force F.
- There will also be a horizontal retarding force opposing the motion of the mower. We'll call this force Fr.
(b) To calculate the horizontal retarding force on the mower, we need to use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. Since the mower is moving at a constant speed, its acceleration is zero. This means the net force acting on the mower is also zero.
The horizontal retarding force (Fr) is equal in magnitude but opposite in direction to the horizontal force applied by the person (F). So, Fr = -F.
(c) The normal force (N) exerted vertically upward by the ground can be found by considering the vertical equilibrium of the mower. Since the mower is not accelerating vertically, the sum of the vertical forces must be zero.
N - mg = 0
N = mg
Substituting the values, we have N = (15.0 kg)(9.8 m/s^2).
(d) To calculate the force the person must exert on the lawn mower to accelerate it from rest to 1.0 m/s in 2.0 seconds, we need to consider Newton's second law again.
Acceleration (a) is given by the change in velocity (Δv) divided by the time taken (Δt). So, a = Δv/Δt = (1.0 m/s)/(2.0 s) = 0.5 m/s^2.
The net force required to accelerate the mower is equal to its mass multiplied by the acceleration.
Fnet = ma = (15.0 kg)(0.5 m/s^2)
Since the retarding force (Fr) is the opposing force acting on the mower,
Fnet = F - Fr
Substituting the values, we can solve for F.
I hope this helps! Let me know if you have any further questions.